Complex surrounding affections for kinetics properties of bio-molecules in two-dimensional free-energy model

Conformational fluctuation is usually the key characteristic of the bio-molecular system, and many kinds of elements from bio-molecules themselves and surroundings can affect this fluctuation. Flexibility is a typical feature of the bio-molecules, and it can also be easily affected by the surroundings. As flexibility is regarded to connect with the conformational fluctuation, it becomes an important entrance to analyze the behavior of the bio-molecules. It is known that the typical kinetic characteristics of bio-molecules are mainly controlled by the rate constant, and these properties are usually dominated by surrounding conditions and configuration features of bio-molecules. We have studied the migration rate of bio-molecules by using the two-dimensional (2D) free-energy landscape and the 2D model that includes the extension coordinate and conformational variable in this work. The 2D generalized Langevin equation with a fractional Gaussian noise or white noise matrix is adopted to reveal the key qualities of the bio-molecular system. The reaction temperature and its flexibility (∆k‡) have been particularly analyzed, and these factors can affect the mean waiting time significantly. Particular attention is paid to distinguish typical discrepancies between normal diffusion and dynamic disorder situations. Our results show that the important conditions from complex surroundings cannot be neglected, and they can be the important factors that affect the kinetic behavior of bio-molecules seriously.